For a given material, Young's modulus is 2.4 times that of rigidity modulus. Its Poisson's ratio is

Options

A. 2.4
B. 1.2
C. 0.4
D. 0.2

Answer

To solve the problem, we need to find the Poisson's ratio (σ) given that Young's modulus (Y) is 2.4 times the rigidity modulus (n). We will use the relationship between these quantities.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Young's modulus (Y) = 2.4 × Rigidity modulus (n)
- We need to find the Poisson's ratio (σ).

2. **Write the Relationship Between Young's Modulus, Rigidity Modulus, and Poisson's Ratio:**
The relationship is given by the formula:
\[ Y = 2n(1 + σ) \]

3. **Substitute the Given Value of Young's Modulus:**
Substitute \(Y = 2.4n\) into the relationship:
\[ 2.4n = 2n(1 + σ) \]

4. **Simplify the Equation:**
Divide both sides by \(n\) (assuming \(n \neq 0\)):
\[ 2.4 = 2(1 + σ) \]

5. **Divide Both Sides by 2:**
\[ 1.2 = 1 + σ \]

6. **Isolate σ:**
Subtract 1 from both sides:
\[ σ = 1.2 - 1 = 0.2 \]

7. **Conclusion:**
The Poisson's ratio (σ) is 0.2.

### Final Answer:
The Poisson's ratio is 0.2.

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